Discontinuous Term Research Articles

Hybrid Difference Scheme for Singularly Perturbed Differential Equation with Discontinuous Source Term

Hybrid Difference Scheme for Singularly Perturbed Differential Equation with Discontinuous Source Term

A computational approach to solving a second-order singularly perturbed Fredholm integro-differential equation with discontinuous source term

A computational approach to solving a second-order singularly perturbed Fredholm integro-differential equation with discontinuous source term

An almost second order uniformly convergent method for a two-parameter singularly perturbed problem with a discontinuous convection coefficient and source term

<p>In this paper, we discuss a higher-order convergent numerical method for a two-parameter singularly perturbed differential equation with a discontinuous convection coefficient and a discontinuous source term. The presence of perturbation parameters generates boundary layers, and the discontinuous terms produce interior layers on both sides of the discontinuity. In order to obtain a higher-order convergent solution, a hybrid monotone finite difference scheme is constructed on a piecewise uniform Shishkin mesh, which is adapted inside the boundary and interior layers. On this mesh (including the point of discontinuity), the present method is almost second-order parameter-uniform convergent. The current scheme is compared with the standard upwind scheme, which is used at the point of discontinuity. The numerical experiments based on the proposed scheme show higher-order (almost second-order) accuracy compared to the standard upwind scheme, which provides almost first-order parameter-uniform convergence.</p>

Piecewise approximate analytical solutions of high-order reaction-diffusion singular perturbation problems with boundary and interior layers

<abstract> <p>This work aims to present a reliable algorithm that can effectively generate accurate piecewise approximate analytical solutions for third- and fourth-order reaction-diffusion singular perturbation problems. These problems involve a discontinuous source term and exhibit both interior and boundary layers. The original problem was transformed into a system of coupled differential equations that are weakly interconnected. A zero-order asymptotic approximate solution was then provided, with known asymptotic analytical solutions for the boundary and interior layers, while the outer region solution was obtained analytically using an enhanced residual power series approach. This approach combined the standard residual power series method with the Padé approximation to yield a piecewise approximate analytical solution. It satisfies the continuity and smoothness conditions and offers higher accuracy than the standard residual power series method and other numerical methods like finite difference, finite element, hybrid difference scheme, and Schwarz method. The algorithm also provides error estimates, and numerical examples are included to demonstrate the high accuracy, low computational cost, and effectiveness of the method within a new asymptotic semi-analytical numerical framewor.</p> </abstract>

Improved dynamic sliding mode control for plate hoisting of cable crane under wind load

In order to quickly eliminate the swing angle of plate hoisting under wind load, an improved dynamic sliding mode control method is proposed in this paper. Firstly, the plate hoisting model under wind load is simplified into a double pendulum system, and the dynamic model of a double pendulum cable crane with wind disturbance is established. To enhance the coupling relationship between trolley displacement and double swing angle, a new coupling state vector for the double pendulum system is defined. On this basis, a dynamic sliding surface is constructed and then an integral function of the system’s discontinuous term is established, essentially ensuring the continuity of the sliding surface and reducing the system’s chattering characteristics. Finally, the stability of the system is rigorously proved by Lyapunov theorem and Barbalat lemma. The simulation and experimental results show that the controller proposed in this paper has a good effect on the anti-swing problem of plate hoisting under wind load.

Adaptive fuzzy sliding mode control of the manipulator based on an improved super-twisting algorithm

The high-precision trajectory tracking and chatter-free performance of the manipulators are of great significance to the improvement of the automation level. Therefore, in view of the problems of chattering and tracking performance degradation of multi-joint manipulators caused by uncertain factors such as external disturbances and modeling errors, an adaptive fuzzy sliding mode control of the manipulator based on an improved super-twisting algorithm is proposed. First, fuzzy control is chosen to approximate the uncertainty of the manipulator model, which reduces the influence of unknown disturbances on the system, and then the adaptive law is utilized to automatically modify and improve the fuzzy rules to enhance the approximation capability; Second, an improved super-twisting algorithm is used on this basis to put the discontinuous term into the integral term to avoid chattering and eliminate the approximation error; Finally, a comparative simulation experiment is carried out with the 3-DOF manipulator as the research object. The experimental results show that the method in this paper improves the convergence speed by up to 69.74% and the tracking error accuracy by up to 85.11% over the fuzzy control based on adaptive reaching law with no chattering and little difference in control inputs, thus verifying the feasibility and superiority of the method.

Robust numerical schemes for time delayed singularly perturbed parabolic problems with discontinuous convection and source terms

This article deals with two different numerical approaches for solving singularly perturbed parabolic problems with time delay and interior layers. In both approaches, the implicit Euler scheme is used for the time scale. In the first approach, the upwind scheme is used to deal with the spatial derivatives whereas in the second approach a hybrid scheme is used, comprising the midpoint upwind scheme and the central difference scheme at appropriate domains. Both schemes are applied on two different layer resolving meshes, namely a Shishkin mesh and a Bakhvalov–Shishkin mesh. Stability and error analysis are provided for both schemes. The comparison is made in terms of the maximum absolute errors, rates of convergence, and the computational time required. Numerical outputs are presented in the form of tables and graphs to illustrate the theoretical findings.

Proximal linearized method for sparse equity portfolio optimization with minimum transaction cost

In this paper, we propose a sparse equity portfolio optimization model that aims at minimizing transaction cost by avoiding small investments while promoting diversification to help mitigate the volatility in the portfolio. The former is achieved by including the ell _{0}-norm regularization of the asset weights to promote sparsity. Subjected to a minimum expected return, the proposed model turns out to be an objective function consisting of discontinuous and nonconvex terms. The complexity of the model calls for proximal method, which allows us to handle the objective terms separately via the corresponding proximal operators. We develop an efficient algorithm to find the optimal portfolio and prove its global convergence. The efficiency of the algorithm is demonstrated using real stock data and the model is promising in portfolio selection in terms of generating higher expected return while maintaining good level of sparsity, and thus minimizing transaction cost.

Determination and Management of Risks for Practices and Procedures in the Elderly (DRIPP): the impact of a comprehensive geriatric evaluation in elderly with diffuse large B-cell lymphoma

IntroductionDiffuse large B-cell lymphoma (DLBCL) treatment in older patients is challenging. The Determination and Management of Risks for Practices and Procedures in the Elderly (DRIPP) is a multidimensional evaluation program that involves patients undergoing oncological treatments. ObjectiveWe aimed to evaluate the overall survival and progression-free survival (PFS) of patients evaluated and those not evaluated by the DRIPP. Materials and methodsRetrospective cohort study, patients > 65 years with DLBCL were included. They were divided into 3 groups: patients with a diagnosis prior to the DRIPP implementation (pre-DRIPP), patients with the DRIPP (DRIPP) and patients with a diagnosis after the DRIPP implementation, but who did not undergo the evaluation (non-DRIPP). ResultsA total of 125 patients were analyzed. Fourteen (11%) patients in the pre-DRIPP group, 74 (59%) in the DRIPP group, and 37 (30%) in the non-DRIPP group. In 43 (58%) patients of the DRIPP group, some drug dose adjustments were made vs. 19 (15%) in the non-DRIPP (p = 0.03). There were no significant differences in terms of discontinuation of treatment or hematological toxicity between groups. The OS and PFS in one year was 64% (95%CI 34–83) and 50% (95%CI 23–72) for the pre-DRIPP group, 82% (95%CI 71–89) and 72% (95%CI 60–81) for the DRIPP group, 58% (95% CI 41–72) and 56% (95% CI 38–70) for the non-DRIPP group, (p = 0.08). The analysis was adjusted for probable confounders and no differences were found. ConclusionsThis is the first study to evaluate the DRIPP as a decision-making tool in patients with lymphoma and showed a trend towards improvement in the OS in evaluated patients.

An equidistributed grid-based second-order scheme for a singularly perturbed Fredholm integro-differential equation with an interior layer

In this study, we introduce and evaluate the effectiveness of the central finite difference coupled with a composite trapezoidal rule on adapted meshes in solving a second-order singularly perturbed Fredholm integro-differential equation with a discontinuous source term. A grid equidistribution technique was employed to address the challenge posed by the perturbation parameter in classical numerical methods. Our approach demonstrated superior precision compared to existing schemes in the literature and achieved second-order uniform convergence.

Efficacy and tolerability of dolutegravir/lamivudine versusdolutegravir/rilpivirine in switching from a three-drug regimen based on nonnucleoside reverse transcriptase inhibitors: A retrospective cohort study.

Real-life comparisons of dolutegravir/rilpivirine (DTG/RPV) and DTG/lamivudine (3TC) regimens in people living with human immunodeficiency virus (PLWHIV) who switched from a standard three-drug regimen based on nonnucleoside reverse transcriptase inhibitors (NNRTIs) are missing.This study aimed to compare DTG/3TC and DTG/RPV in virologically suppressed patients (HIV-RNA < 50 copies/mL) coming from any NNRTI-based regimen in terms of discontinuation due to virologic failure (VF) discontinuation rates due to all causes, and adverse events. As a secondary outcome, we evaluated the difference in creatinine, total cholesterol, CD4, and triglycerides from baseline to weeks 48 after the switch.Of the 415 PLWHs included in the study, 278 (66.9%) switched to DTG/3TC, and 137 (33.1%) switched to DTG/RPV. Overall, 48 PLWHs (11.6%) discontinued the treatment:38 with DTG/3TC and 10 with DTG/RPV with similar discontinuation rates: 5.01 × 100 py (95% confidence interval [CI] 3.64-6.94)and 4.66 × 100 py (95% CI 2.51-8.67), respectively. The most common reason for discontinuation was toxicity (26 patients, 22/278 [7.9%]in the DTG/3TC group and 4/137 [2.9%]in the DTG/RPV group), mainly neurologic toxicity (never above grade 2). We found no differences in discontinuation rates due to treatment adverse events. Two study participants experienced virological failure in the DTG/3TC arm. We observed no significant difference in CD4 cell counts, lipid parameters, or renal function between the two groups at 48 weeks.This study demonstrated that, in clinical practice, a two-drug regimen with DTG/3TC or DTG/RPV is characterized by a low discontinuation rate and VF in virologically suppressed PLWHs switched from an NNRTI-based three antiretroviral drugs regimen.

Representatives of the Central Authority and County Administration in Transylvania (1867–1925)

The transition from the administrative system of the Habsburg monarchy to that of the successor nation-states after World War I has traditionally been analysed in terms of discontinuity, or even rupture. In our research, which focuses on the specific case of Transylvania, we demonstrate that both the development of a centralised administrative system and the relationship between the state authority and local autonomies were characterised by continuity rather than change. In both the Hungarian and the Romanian state, the key institution involved in the process of diminishing local self-government was the representative of the central power in the territory (the lord lieutenant until 1918 and later the prefect). The gradual expansion of his prerogatives over institutions and county officials began in Hungary in the early 1870s, and continued until the interwar period in Romania; this was a process that extended beyond the changes in the political and state regime in 1918. Thus, for interwar Transylvania, administrative centralisation in the French tradition did not represent a paradigm shift, but instead the continuation and acceleration of an already quite advanced process that the Hungarian state, which had been eager to modernise its administrative structures, had already introduced 50 years earlier.

AFS control system research of distributed drive electric vehicles by adaptive super-twisting sliding mode control

To solve the problems of serious buffeting in traditional sliding mode control and difficulty in obtaining the derivative information of the system sliding mode surface, a distributed drive electric vehicles active front steering (AFS) control method based on adaptive super-twisting sliding mode control (ASTSMC) is proposed. Taking the yaw rate deviation as the state quantity, the stable and convergent sliding mode surface is designed to obtain the equivalent control input of the front wheel angle. The sliding mode function information is substituted into the parameters of the super-twisting algorithm; the discontinuous term is kept in the integrand function to keep the control signal continuous and weaken the system chattering; the adaptive control law is added to design the AFS controller. The co-simulation results of Matlab/Simulink and Carsim show that ASTSMC can reduce the yaw rate by 40.59% compared with no control under step steering condition. Compared with the sliding mode controller, ASTSMC has optimized the sideslip angle by 5.41% under the double line shifting condition.

Seismic structure of the Eastern European crust and upper mantle from probabilistic ambient noise tomography

The Eastern European lithosphere is a natural laboratory to study continental formation and evolution through time, comprising Archean continental remnants, Proterozoic rifts and belts, and younger accreted terranes. We investigate the seismic structure of the East European Craton (EEC) crust and uppermost mantle, and the transition from Precambrian to Phanerozoic Europe across the Trans European Suture Zone (TESZ) using probabilistic transdimensional ambient noise tomography. We cross-correlate noise recorded at broadband seismic stations from Eastern, Northern, and Central Europe, remove earthquake signals using continuous wavelet transform, and extract Rayleigh wave phase velocity dispersion curves. We invert these for the highest resolution shear wave velocity model of the Eastern European lithosphere to date, using Markov chain Monte Carlo Bayesian inversion. Our shear wave velocity model exhibits spatial correlation with major tectonic units and bears similarities with active seismic survey profiles in terms of seismic velocity patterns and main discontinuities. The crust thickens across the TESZ boundary and the mantle is seismically faster than beneath younger terranes, consistent with a less dense Precambrian lithosphere in the EEC. The crust and lithosphere beneath the Pannonian region is hyper-extended but the adjacent Transylvanian basin crust shows significant heterogeneity. The Precambrian building blocks of the EEC exhibit contrasting seismic fabrics. The Baltic orogens of Fennoscandia are underlain by uniform crust with a flat Moho, while Sarmatia shows alternating high and low velocity layers and a regional south-dipping crustal boundary from beneath the Ukrainian Shield towards the Crimean Peninsula. The last observation supports a geodynamic style driven by horizontal rather than vertical tectonics, with fundamental implications for the formation and evolution of early continents.

Fixed-time generalized super-twisting control for path tracking of autonomous agricultural vehicles considering wheel slipping

Efficient path tracking control for autonomous agricultural vehicles (AAVs) is the key technology for realizing agriculture 4.0 and precision agriculture, which makes smart farms more sustainable, profitable, and eco-friendly. It is well recognized that model nonlinearity, unknown disturbances, and wheel slipping are common problems in practical AAV systems in operation. To tackle these issues and improve the path tracking performance, a novel fixed-time generalized super-twisting control scheme is proposed for AAVs in this paper. First, a fixed-time integral sliding mode surface is designed for the considered vehicle by fusing the lateral offset and heading offset together. Then, an innovative auxiliary system dynamics is constructed to collaborate with the foregoing sliding mode surface, compensating for the adverse effects of wheel slipping effectively. Subsequently, based on the kinematic offset model of AAVs, a new type of generalized super-twisting controller is designed to achieve superior path tracking with robustness. Unlike existing super-twisting controllers, the generalized super-twisting continuous controller can fully eliminate chattering by replacing the previous discontinuous terms with a nonsmooth term. Further, rigorous theoretical analysis is conducted by raising a fresh Lyapunov function to verify the closed-loop control system stability. Finally, extensive field experiments have been carried out to show that the proposed control scheme significantly outperforms typical comparative control schemes.

Saturated exponential super‐twisting sliding mode control for bottom‐following of biomimetic underwater vehicles with unmeasured velocities

AbstractThis article addresses the bottom‐following problem for biomimetic underwater vehicles without translational velocity measurements in the presence of complex uncertainties and actuator saturation. A novel saturated exponential super‐twisting algorithm based integral terminal sliding mode control (SESTA‐ITSMC) scheme is created to ensure fast convergence and strong robustness as well as attenuate the chattering of actuators. Salient features are as follows. Instead of discontinuous term in the conventional super‐twisting algorithm, a novel SESTA is developed by incorporating a fractional power term, which ensures that the system achieves a faster transient response, effectively eliminating the chattering phenomenon. Then, to deal with the unknown states and further improve the anti‐interference ability of the system, the finite‐time dual estimator is devised to fast and precisely estimate the translational velocities and lumped uncertainties. Finally, a finite‐time anti‐windup auxiliary system is proposed to compensate for the saturation constraints on actuators in real time. Finite‐time convergence of estimation errors and bottom following errors is guaranteed by the Lyapunov stability theory. Comparative simulation results fully demonstrate the excellence of the proposed SESTA‐ITSMC scheme.

Adaptive parameter learning and neural network control for uncertain permanent magnet linear synchronous motors

This work aims to achieve accurate parameter estimation and intelligent control of a permanent magnet linear synchronous motor (PMLSM) with unknown parameters, nonlinearities, and disturbances. To address it, we propose a novel adaptive control method composed of a new estimation error-based learning strategy and a neural network (NN)-based adaptive sliding mode controller. An augmented NN with a friction model and a force ripple model is constructed to handle the uncertainties in PMLSM. The proposed learning law that contains leakage terms driven by estimation errors calculates the unknown parameter and NN’s weights online. Especially the gain of the discontinuous term in the learning law is adjusted by the presented update law to reduce the chattering of learned parameters. The controller handles the residual error and external disturbance. Different from the existing methods, the proposed one needs no boundary information of uncertainties in both the controller and parameter-learning strategy. The proposed method is finite-time semi-global uniformly and ultimately bounded (FTSGUUB), which is analyzed by designing a Lyapunov function. Finally, numerical simulations are carried out to validate the parameter learning and control accuracy of the proposed method.

Stability and Stabilization of T–S Fuzzy Time-Delay Systems Under Sampled-Data Control via New Asymmetric Functional Method

This paper studies the stability and stabilization of Takagi-Sugeno (T-S) fuzzy time-delay systems under sampleddata control via a new asymmetric Lyapunov-Krasovskii functional (LKF) method. The method improves the common symmetric basic functional term. Besides, we improve the loopedfunctional term and the discontinuous functional term through combining the integral about time delay and each sampling interval, respectively. Based on the above new approaches, we present the stability and stabilization results with less conservativeness than the literature through linear matrix inequalities (LMIs). In the process, we introduce a simplification approach for stabilization of sampled-data control, which effectively reduces the computational complexity of results. At last, we provide three examples to verify the effects and advantages of our results.

Potentiality of the HOFiD_bvp code in solving different kind of second order boundary value problems

The aim of this paper is to present the potentiality of the code HOFiD_bvp based on high order finite difference, following the approach of the boundary value methods and the upwind methods. Strategies, as variable stepsize and variable order, that helps to handle with solutions of singular perturbation problems, so as the continuation strategy applied for solving nonlinear problems, will be discussed. Now, the method is suitable to solve second order scalar boundary value problems, not only singularly perturbed with one and two parameters, but also problems with discontinuous source terms. Concerning that point some numerical tests will be taken in consideration in order to show the potentiality of the code.

Spatiotemporal sampled-data fuzzy control for switched singularly perturbed PDE systems with average dwell-time switching mechanism

This paper investigates a spatiotemporal sampled-data fuzzy control strategy for switched singularly perturbed partial differential equation (PDE) systems, where the systems’ operation modes obey average dwell-time switching mechanism. To efficiently deal with nonlinear terms and guarantee the system stability for the considered systems, a spatiotemporal sampled-data fuzzy control scheme is developed. Furthermore, based on the fact that mode mismatch phenomena during switching and sampling, through formulating novel Lyapunov functionals (LFs) with the discontinuous terms and mode-dependent two-sided looped-functionals, which can fully utilize the state information of the sampling period, a new exponential stability criterion is provided for the target systems. Finally, an example is provided to prove the validity of the proposed control approach.